In Paper I, we presented a new model of the velocity distribution function for protons composing a stellar atmosphere expanding in interstellar space, valid from collisional to collisionless regions. In this paper, the set of generalized transport equations associated with this model and the closure assumptions for higher order velocity moments are provided for 9 and 16 moment approximations. The study of the properties of such a set of transport equations in the collisionless limit is presented and discussed. A comparison with the similar bi-Maxwellian approximation is made using two kinds of analysis, in the context of an application to solar wind expansion. Our model is better adapted to high values of the heat flux and thus is able to provide a macroscopic parameter evolution for stellar atmosphere expansion in a state far from local equilibrium, as well as for the expansion of planetary polar winds.